Applied Mathematics for Business
Mock Exam
Course Introduction
Applied Mathematics for Business introduces students to essential mathematical concepts and techniques used in various business contexts. Topics include linear equations, functions, matrices, linear programming, financial mathematics, probability, and statistics. Through real-world business applications and case studies, students learn how to analyze and solve problems related to profit maximization, cost minimization, investment decision-making, and data interpretation, equipping them with practical skills for quantitative reasoning in managerial and financial environments.
Recommended Textbook
Introductory Mathematical Analysis for Business Economics and the Life and Social Sciences 14th
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Chapter 1: Review of Algebra
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Sample Questions
Q1) Multiply and simplify: (y - 3)(y + 7)
Answer: 11ea83f6_629e_828c_b5a5_b38914f55f60_TB6578_11_TB6578_11 + 4y - 21
Q2) What is the sales tax paid on an item whose total receipt was $100.75 and whose sales tax rate was 5.5%?
Answer: $95.50
Q3) Multiply and simplify: (z - 5)(z - 1)
Answer: 11ea83f6_629e_828d_b5a5_95eb3d1118ba_TB6578_11_TB6578_11 - 6z + 5
Q4) Simplify: (-15)÷ (-5)
Answer: 3
Q5) Multiply and simplify: (x + 2)(x + 4)
Answer: 11ea83f6_629e_828b_b5a5_6fb8e7f228b8_TB6578_11_TB6578_11 + 6x + 8
Q6) Completely factor: 5x - 5
Answer: 5(x - 1)
Q7) Solve: (10 - 2x)(5 - x)= 50
Answer: x = 0,10
Q8) Multiply and simplify: (t + 3)(t - 3)
Answer: 11ea83f6_629e_5b78_b5a5_71445df03c1f_TB6578_11_TB6578_11 - 9
Q9) Simplify: (-4)÷ (-2 - 10)
Answer: 11ea83f6_6296_e16e_b5a5_814108335f17_TB6578_11_TB6578_11
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Chapter 2: Applications and More Algebra
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Sample Questions
Q1) Express the sum in summation notation.
7 + 11 + 15 + 19 + 23 + 27 + ...+ 67
Answer: 11ea83f6_62c0_143c_b5a5_531889a8e3eb_TB6578_11_TB6578_11
Q2) Express the sum in summation notation.
4 + 6 + 8 + 10 + 12 + 14 + 16
Answer: 11ea83f6_62bf_50d3_b5a5_cb85d5c95599_TB6578_11_TB6578_11
Q3) The owner of an 85 unit apartment building must raise the rent to cover an increase in property taxes of $9000 per year.At the current rent of $600 per month,each $30 per month increase will create one vacancy with no possibility of filling it.By how much should he raise the rent for these apartments?
Answer: $150 or $1800
Q4) A metallurgist is preparing 63 kg of an alloy.It must consist of 3 parts aluminum and 4 parts copper.How much of each metal should be used?
Answer: 27 kg aluminum and 36 kg copper
Q5) A company manufactures hair dryers.The manufacturing cost is $9 per unit with a fixed cost of $16,000.A hair dryer sells for $15.If the company wants to earn a profit of $50,000,how many dryers must be sold?
Answer: 11,000
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Chapter 3: Functions and Graphs
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Sample Questions
Q1) Brett rented a bike from a rental shop and rode at a constant rate of 12 mph for 2.5 hours along a bike path,and then returned along the same path at the same rate.Write an absolute-value function to represent Brett's distance from the rental shop as a function of time.
Answer: f(x)= - 11ea83f6_62ca_4d91_b5a5_87b3b9abae12_TB6578_11_TB6578_11 + 30
Q2) Find the domain of the function f(x)= 6.
Answer: all real numbers
Q3) A coat costs x wholesale.The price the store pays is given by the function s(x)= 1.2x where x is the wholesale price.The price the customer pays is c(x)= 2x + 50 where x is the price the store pays.Write a composite function to find the customer's price as a function of the wholesale price.
Answer: c(s(x))= 2.4x + 50
Q4) Ellen's health plan has a $10.00 copayment for complete pregnancy care.Let x represent the number of prenatal visits and y represent her cost for the pregnancy.Write an equation which represents the relationship between her cost for the pregnancy and her number of prenatal visits; describe the graph of this equation,and identify the intercepts.
Answer: y = 10; horizontal line; no x-intercept; y-intercept (0,10)
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Chapter 4: Lines parabolas and Systems
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Sample Questions
Q1) A manufacturer sells his product at $23 per unit,selling all he produces.His fixed cost is $18,000 and his variable cost per unit is $18.50.The level of production at which the manufacturer breaks even is
A) 3000 units.
B) 3500 units.
C) 4000 units.
D) 4500 units.
E) 5000 units.
Q2) A coordinate map of a zoo shows the outdoor aviary at (2,4)and the snack bar at (2,8).What is an equation for the line between these two locations?
Q3) How much of each of a 25% (by volume)chemical solution and a 32% solution must be combined to make 75 cubic centimeters of a 28% solution?
Q4) Show that the points A(0,0),B(0,3),C(8,5),and D(12,3)are the vertices of a trapezoid.(A trapezoid is a four-sided figure with exactly two sides parallel.)
Q5) Determine whether the following lines are parallel,perpendicular or neither.
0.1x - 7y + 81 = 0
2x - 140y + 9 = 0
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Chapter 5: Exponential and Logarithmic Functions
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Sample Questions
Q1) An earthquake which is 48,000 times as intense as a zero-level earthquake has a magnitude on the Richter Scale which is 1.7 less than the intensity of another earthquake.What is the intensity of the other earthquake?
Q2) If $500 is invested for 3 years at 7% compounded semiannually,then the compound interest at the end of the period is
A) $112.52.
B) $114.63.
C) $120.37.
D) $122.56.
E) $150.36.
Q3) Suppose $2000 is invested at 6.5% compounded monthly.
(a)Find the value of the investment after 5 years.
(b)Find the value of the interest which was earned over the first 5 years.
Q4) Your friend started a savings plan with 2 pennies and each day he doubled the amount saved.Later you started a savings plan with 4 pennies and each day you quadrupled the amount saved.Your friend has been saving for 6 less than 3 times as many days as you.In two days you will put the same amount in savings as your friend.How many days have you been saving?
Q5) Express 2 ln 3 - ln 4 as a single logarithm.
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Chapter 6: Mathematics of Finance
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Sample Questions
Q1) If $1,000 is invested at a nominal rate of 4% compounded quarterly for 5 years,find the compound amount.
Q2) If an initial investment of $4000 grows to $4884 in five years,find the nominal rate of interest,compounded monthly,that was earned by the money.
Q3) At what nominal rate of interest,compounded quarterly,will an investment double in 15 years?
Q4) Find the present value of a future value of $4,200 due in 11 years at a nominal rate of 6% compounded monthly.
Q5) A debt of $12,000,which is due 10 years from now,is instead to be paid off by four payments: $3000 now,$2000 in 3 years,$2000 in 6 years,and a final payment at the end of 8 years.What would this payment be if an interest rate of 5.5% compounded semiannually is assumed?
Q6) $200 is invested at the rate of 3.5% compounded quarterly for six and a half years.How many terms are in the geometric sequence formed by the amounts at the end of each quarter?
Q7) Find the effective rate that corresponds to an interest rate of 5% compounded daily. To view all questions and flashcards with answers, click on the resource link above.
Page 8
Chapter 7: Matrix Algebra
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Sample Questions
Q1) Use the matrix operations on a graphing calculator to show that A + (B + B) + C.
C) = (A +
Q2) Find the amount of each raw material the manufacturer will need to fill the orders.
Q3) What is the change in sales between 1994 and 1996?
Q4) The spa staff determines that a client should take 190% of the RDA of vitamin A,150% of the RDA of vitamin C,and 120% of the RDA of vitamin D each day.How many tablets of each supplement should he take each day?
Q5) A manufacturer who produces products A,B,and C is only interested in tracking labor costs.What is the order of the matrix he would use?
Q6) Show that A + B = B + A.
Q7) Use the matrix operations on a graphing calculator to find her income if increasing it by 20% would cause an increase in profit of 50%.(Round to the nearest thousand dollars.)
Q8) What would her income be if increasing it threefold would cause her profit to be five times as large? (Round to the nearest thousand dollars.)
Q9) EF
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Chapter 8: Linear Programming
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Sample Questions
Q1) Maximize
Z = 4x + y subject to -x + y 2
3x + y 18 x,y 0.
Q2) A store sells two types of calculators.In order to cover overhead,it must sell at least 40 calculators total per week,and in order to satisfy distribution requirements,it must sell at least twice as many of type II as type I.Write a system of inequalities to describe the situation.Let x be the number of type I that it sells in a week and y be the number of type II that it sells in a week.Find the region described by the system of linear inequalities.
Q3) Maximize
Z = 2x - 3y subject to 2x + y 1
x - y 1
x,y 0.
Also find the corner point where the value of z is attained.
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10
Chapter 9: Introduction to Probability and Statistics
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Sample Questions
Q1) From a lot of ten computers,two are selected for extensive testing.In how many ways can the selection be made?
Q2) The winner of a contest can choose any two of six different prizes.How many choices are possible?
A) 15
B) 20
C) 25
D) 30
E) 34
Q3) In a certain town,30% of eligible voters are Democrats,40% are Republicans,and the rest are Independents.In the last election,20% of the Democrats,10% of the Republicans,and 30% of the Independents voted.If an eligible voter is chosen at random,what is the probability that he or she is a Republican who voted?
A) 0.4
B) 0.06
C) 0.12
D) 0.04
E) 0.1
Q4) In how many ways is it possible to answer a six-question true-false examination.
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Chapter 10: Additional Topics in Probability
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Sample Questions
Q1) P(X = 6); n = 13,p = 0.5
A) 0.2095
B) 0.3142
C) 0.2723
D) 0.0156
Q2) An urn contains three red and one green marble.Two marbles are randomly drawn in succession without replacement.If X is the number of red marbles that are drawn and f is the distribution of X,find f(0),f(1),and f(2).
Q3) Suppose that you pay $1 to play a game in which a pair of fair dice are rolled.For each 2 that shows on a die you receive $2.To the nearest cent,your expected loss on each play is
A) $0.67.
B) $0.33.
C) $0.25.
D) $0.15.
E) $0.07.
Q4) A fair die is rolled four times.What is the probability that exactly three 2's appear?
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12
Chapter 11: Limits and Continuity
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Sample Questions
Q1) Find: lim 15 x 8
Q2) Suppose that the rent for an apartment in a city with rent control is $540 per month.Show that the rent function R(t)= 540 is continuous at t = 3.
Q3) Suppose that the rent for an apartment in a city with rent control is $740 per month.Show that the rent function R(t)= 740 is continuous at t = 3.
Q4) Solve: (x + 6)(x - 1)(x - 4) 0
Q5) Use the definition of continuity to show f(x)= 2x + 3 is continuous at x = -1.
Q6) Suppose that the rent for an apartment in a city with rent control is $540 per month.Show that the rent function R(t)= 540 is continuous at t = 5.
Q7) Find: \(\lim_{x \rightarrow 5}\) \(\frac{x^{2}}{h}\)
Q8) Find the value(s)of x for which f(x)= 10 is discontinuous.
Q9) Use the definition of continuity to show f(x)= 2 is continuous at x = 5.
Q10) Consumers will purchase q units of a certain product when the price is 340 - 2q dollars per unit.How many units must be sold in order that sales revenue be no less than $14,000?
Q11) Solve: (x - 1)(x + 2)(x - 3) 0
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Chapter 12: Differentiation
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Sample Questions
Q1) The concentration of acid in a buffer solution is given by A = 0.8.Graph this function on your graphing calculator and describe its slope.
Q2) If a function is differentiable at x = a,then it is continuous at x = a.
A)True
B)False
Q3) A bus company will plan a group trip for groups of 10 or larger.If the group is exactly 10,the cost is $50 per person.The company offers to discount each person's ticket by $2 for each addition to the group above 10.The revenue for the bus company is given by: R(x)= (10 + x)(50 - 2x)where x is the number of additional people above 10.Find the marginal revenue function using the product rule.
Q4) Find the rate of change of the area of a square with respect to its one side.Evaluate it when side = 4 units.
Q5) If the revenue function is given by R(x)= 11x + 9,find the derivative of the revenue function (this is called the marginal revenue).
Q6) The height of a boulder just sitting on a 30-foot cliff is given by y = 32.Graph this function on your graphing calculator and describe its slope.
Q7) Differentiate: g(x)= (x - 8)(2x - 7)(x + 5)
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Chapter 13: Additional Differentiation Topics
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Sample Questions
Q1) The total cost for a product is given by C(x)= 36 + 5 ln(3x + 9).Find the rate of change of C''(x).
Q2) Determine the point elasticity of the demand equation pq + p + 50q = 10,000 when p = 200.
Q3) The total cost for a product is given by C(x)= 900 + 8 ln(3x + 7).Find the rate of change of C''(x).
Q4) The total cost for a product is given by C(x)= 212 + 3 ln(2x + 1).Find the rate of change of C''(x).
Q5) The total cost for a product is given by C(x)= 1750 + 300 ln(x + 2).Find the rate of change of C''(x).
Q6) If the position of a particle moving along the x-axis at a given time is given by x(t)= 5t + 11,find all the higher-order derivatives of this function.
Q7) If the point elasticity of demand for a product is -2.3 and the price of the product increases 3%,what is the approximate percentage decrease in demand?
Q8) An experiment was set up to find a relationship between weight and systolic blood pressure in children.It was found that p(x),the systolic blood pressure,was approximately p(x)= 17.5(1 + ln x),where x is the child's weight in pounds.Find p'(x).
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Chapter 14: Curve Sketching
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Sample Questions
Q1) A real estate firm owns 70 apartments.At $200 per month each apartment can be rented.However,for each $10 per month increase,there will be two vacancies with no possibility of filling them.What rent per apartment will maximize monthly revenue?
Q2) A company owns an apartment building containing 80 units.If the company charges $300 per month rent,then all units can be rented out,and for every increase of $10 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?
Q3) A cable TV company has 500 customers paying $20 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.
Q4) Find two numbers whose sum is 30 and whose product is a maximum.
Q5) An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.
Q6) Find two positive numbers whose product is 25 and whose sum is a minimum.
Q7) Find all the critical values of f(x)= x ln x.
Q8) Find two numbers whose sum is 50 and such that the product of one of them and five more than the other is a maximum.
Page 16
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Chapter 15: Integration
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Sample Questions
Q1) If y'' = 6x + 2 and y'(1)= 2 and y(1)= 2,find y.
Q2) If y = x ln x,then dy =
A) 1 + ln x.
B) (1 + ln x) dx.
C) x + ln x.
D) (x + ln x) dx.
E) none of the above
Q3) Use differentials to approximate: ln(0.95).
Q4) By using differentials,an approximation of ln(1.03)is
A) -0.01.
B) 0.01.
C) 0.02.
D) 0.03.
E) 0.04.
Q5) Use differentials and C = 250 + 0.30x to approximate the change in the cost C (in dollars)to produce x pounds of candy if the number of pounds of candy increases from 10 pounds to 10.6 pounds.
Q6) If the marginal cost (in dollars)for a company is C'(x)= 200,and the cost for producing 8 units is $2250,that is C(8)= 2250,then find C(x).
Page 17
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Chapter 16: Methods and Applications of Integration
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Sample Questions
Q1) An ecologist has determined that a local metro-park has food to support up to 200 rabbits at any given time.Now,from observations,he estimates that there are 20 rabbits.One week from now,he estimates that there are 30 rabbits.Assuming logistic growth,find the logistic function that will model this rabbit population.
Q2) The demand equation for a certain product is p = 400 - 2q,where p is the price per unit (in dollars)for q units.If its supply equation is p = q + 100,then the consumers' surplus when market equilibrium is established is
A) $9000.
B) $9500.
C) $10,000.
D) $10,500.
E) $11,000.
Q3) Find the exact area of the region bounded by the graphs of y = -x,y = 2x,y = 1,and y = 2.Also sketch the region.
Q4) If 55% of the initial amount of a radioactive sample remains after 10 hours,find the decay constant and the half-life of the element.
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Page 18
Chapter 17: Continuous Random Variables
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Sample Questions
Q1) Suppose X is normally distributed with = 80 and = 15.Without using tables,approximate P(50 < X < 80).
Q2) If X is a normal random variable with = 16 and = 2,determine the Z-value that corresponds to X = 23.
Q3) The life (in hours)of light bulbs of a certain brand is normally distributed with mean 1200 and standard deviation 100.What percentage of such bulbs will burn more than 1250 hours?
A) 13.62
B) 20.47
C) 30.85
D) 41.73
E) 48.26
Q4) If X is normally distributed with mean and standard deviation ,then what is the approximate probability that - 2 X + 2 ?
A) 0.5
B) 0.68
C) 0.95
D) 0.997
E) 0.999
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Chapter 18: Multivariable Calculus
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Sample Questions
Q1) An open rectangular cardboard box is to have a volume of 4 cubic feet.Find the dimensions of the box so that the amount of cardboard is minimized.
Q2) Use the method of Lagrange multipliers to determine the critical points of f(x,y)= x + 2y subject to the constraint xy = 8.
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